Abstract: | While alternating direction implicit (ADI) collocation methods have been used for several years to solve parabolic problems in several space variables, no convergence analysis has been derived for any of these methods. We formulate and rigorously analyze ADI collocation schemes applied to the inhomogeneous heat and wave equations on the unit square subject to homogeneous Dirichlet boundary conditions and appropriate initial conditions. We prove that each method is second-order accurate in time and of optimal accuracy in space in the L2 and H01 norms. Numerical experiments confirm the predicted rates of convergence. © 1993 John Wiley & Sons, Inc. |